हिंदी

Check the validity of the following statement.p: 125 is divisible by 5 and 7. - Mathematics

Advertisements
Advertisements

प्रश्न

Check the validity of the following statement.
p: 125 is divisible by 5 and 7.

योग
Advertisements

उत्तर

Given that p: 125 is divisible by 5 and 7.

Let q: 125 is divisible by 5.

And r: 125 is divisible by 7.

Here q is true and r is false.

⇒ q ∧ r is false.

Hence, p is not valid.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 14: Mathematical Reasoning - Exercise [पृष्ठ २६५]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 14 Mathematical Reasoning
Exercise | Q 13.(i) | पृष्ठ २६५

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Show that the statement

p: “If x is a real number such that x3 + 4= 0, then x is 0” is true by

(i) direct method

(ii) method of contradiction

(iii) method of contrapositive


Show that the following statement is true by the method of contrapositive.

pIf x is an integer and x2 is even, then x is also even.


Find out the sentence are statement and are not. Justify your answer.

 This sentence is a statement.


Find out the sentence are statement and are not. Justify your answer.

 Mathematics is difficult.


All birds sing.


 Some even integers are prime.


Write the negation of the statement:

r : There exists a number x such that 0 < x < 1.

 

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
 There exist real numbers a and b for which a + b = b + a.


Find the component statement of the compound statement:
 The sky is blue and the grass is green.


Find the component statement of the compound statement:

All rational numbers are real and all real numbers are complex.


Find the component statement of the compound statement:

 25 is a multiple of 5 and 8.

 

Write the component statement of the compound statement and check whether the compound statement is true or false:

All rational numbers are real and all real numbers are not complex.


Write the component statement of the compound statement and check whether the compound statement is true or false:

 x = 2 and x = 3 are the roots or the equation 3x2 − x − 10 = 0.


Write the component statement of the compound statement and check whether the compound statement is true or false:

The sand heats up quickly in the sun and does not cool down fast at night.

 

Write the negation of  statement:

For every x ϵ Nx + 3 < 10


Write of the statement in the form "if p, then q". 

You can access the website only if you pay a subscription fee.

 


Write of the statement in the form "if p, then q". 

 The game is cancelled only if it is raining.


Write of the statement in the form "if p, then q". 

 Whenever it rains it is cold.


Determine whether the argument used to check the validity of the following statement is correct:
p : "If x2 is irrational, then x is rational"
The statement is true because the number x2 = π2 is irrational, therefore x = π is irrational.


Which of the following statements are compound statements 

“2 is both an even number and a prime number”


Which of the following statements are compound statements 

“9 is neither an even number nor a prime number”


Identify the component statements and the connective in the following compound statements.

2 is a positive number or a negative number.


Write negation of the statement
“Everyone who lives in India is an Indian”


Rewrite the following statements in the form of conditional statements:

Mohan will be a good student if he studies hard.


Translate the following statements in symbolic form:
If x = 7 and y = 4” then x + y = 11.


Form the biconditional of the following statements :
p: Today is 14th of August
q: Tomorrow is Independence day


Identify the quantifiers and write the negation of the following statements:
There exists a number which is equal to its square.


Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.


Which of the following sentences are statements? Justify

Every set is an infinite set.


Which of the following sentences are statements? Justify

Every square is a rectangle.


Which of the following sentences are statements? Justify

Sum of opposite angles of a cyclic quadrilateral is 180°.


Find the component statements of the following compound statements.

Number 7 is prime and odd.


Translate the following statements into symbolic form

Either x or x + 1 is an odd integer.


Translate the following statements into symbolic form

Either x = 2 or x = 3 is a root of 3x 2 – x – 10 = 0


Write down the negation of following compound statements

A triangle has either 3-sides or 4-sides.


Write down the negation of following compound statements

35 is a prime number or a composite number


Identify the Quantifiers in the following statements.

For every natural number x, x + 1 is also a natural number.


Identify the Quantifiers in the following statements.

There exists a statement in above statements which is not true.


Which of the following is the conditional p → q?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×